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Related Concept Videos

Statistical Hypothesis Testing01:16

Statistical Hypothesis Testing

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Hypothesis testing is a critical statistical procedure facilitating informed, evidence-based decisions. It begins with a hypothesis, which is a tentative explanation, or a prediction about a population parameter. This hypothesis can be either a null hypothesis (H0), indicating no effect or difference, or an alternative hypothesis (Ha), suggesting an effect or difference.
Statistical significance measures the probability that an observed result occurred by chance. If this probability, known as...
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Accuracy and Errors in Hypothesis Testing01:13

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Hypothesis testing is a fundamental statistical tool that begins with the assumption that the null hypothesis H0 is true. During this process, two types of errors can occur: Type I and Type II. A Type I error refers to the incorrect rejection of a true null hypothesis, while a Type II error involves the failure to reject a false null hypothesis.
In hypothesis testing, the probability of making a Type I error, denoted as α, is commonly set at 0.05. This significance level indicates a 5%...
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Null and Alternative Hypotheses01:16

Null and Alternative Hypotheses

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The actual hypothesis testing begins by considering two hypotheses. They are termed  the null hypothesis and the alternative hypothesis. These hypotheses contain opposing viewpoints.
The null hypothesis, denoted by H0 is a statement of no difference between the variables—they are not related. This can often be considered the status quo. As  a result if you cannot accept the null, it requires some action.
The alternative hypothesis, denoted by H1 or Ha, is a claim about the...
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Decision Making: Traditional Method01:14

Decision Making: Traditional Method

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The process of hypothesis testing based on the traditional method includes calculating the critical value, testing the value of the test statistic using the sample data, and interpreting these values.
First, a specific claim about the population parameter is decided based on the research question and is stated in a simple form. Further, an opposing statement to this claim is also stated. These statements can act as null and alternative hypotheses, out of which a null hypothesis would be a...
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Hypothesis: Accept or Fail to Reject?01:17

Hypothesis: Accept or Fail to Reject?

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The outcome of any hypothesis testing leads to rejecting or not rejecting the null hypothesis. This decision is taken based on the analysis of the data, an appropriate test statistic, an appropriate confidence level, the critical values, and P-values. However, when the evidence suggests that the null hypothesis cannot be rejected, is it right to say, 'Accept' the null hypothesis?
There are two ways to indicate that the null hypothesis is not rejected. 'Accept' the null...
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What is a Hypothesis?01:14

What is a Hypothesis?

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A hypothesis can be a simple sentence or statement about a property or any phenomenon observed or predicted for a population. It is usually a claim about a  property of the population. It can be stated for any field observations or experiments. A hypothesis statement cannot be said to be right or wrong as it is merely a statement. It needs to be tested through an elaborate data collection process and an appropriate statistical test. A hypothesis should be a general but not a vague...
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Evidence-based Knowledge Synthesis and Hypothesis Validation: Navigating Biomedical Knowledge Bases via Explainable AI and Agentic Systems
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Assessing evidence and testing appropriate hypotheses.

Norman Fenton1

  • 1School of Electronic Engineering and Computer Science, Queen Mary University of London, London E1 4NS, United Kingdom; Agena Ltd, 11 Main Street, Caldecote, Cambridge CB23 7NU, United Kingdom.

Science & Justice : Journal of the Forensic Science Society
|December 16, 2014
PubMed
Summary
This summary is machine-generated.

Choosing the right prosecution hypothesis is vital for accurate probabilistic reasoning. Incorrectly framing the hypothesis, such as "double murder" instead of "at least one murder," significantly alters evidence interpretation and conclusions.

Keywords:
BayesHypothesesLikelihood ratioProbabilistic evidence

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Area of Science:

  • Forensic Science
  • Probability Theory
  • Legal Reasoning

Background:

  • Probabilistic reasoning is essential for evaluating evidence in legal contexts.
  • The formulation of hypotheses significantly impacts the interpretation of evidence and derived probabilities.
  • A real case is used to illustrate the impact of hypothesis selection on probabilistic arguments.

Purpose of the Study:

  • To demonstrate how the choice of prosecution hypothesis affects probabilistic reasoning.
  • To highlight the importance of selecting the most appropriate alternative hypothesis in legal evidence evaluation.
  • To illustrate the sensitivity of posterior probabilities to hypothesis definition.

Main Methods:

  • Comparative analysis of probabilistic arguments under different hypothesis formulations.
  • Calculation of prior odds for defense vs. prosecution hypotheses.
  • Evaluation of likelihood ratios for given evidence.

Main Results:

  • The prior odds favoring the defense hypothesis (Sudden Infant Death Syndrome) over the "double murder" hypothesis were 30:1.
  • The prior odds favoring the defense hypothesis over the "at least one murder" hypothesis were 5:2.
  • A likelihood ratio of 5 for the prosecution hypothesis led to vastly different posterior probabilities depending on the chosen alternative hypothesis.

Conclusions:

  • The selection of an appropriate alternative hypothesis is critical in probabilistic legal reasoning.
  • Subtle changes in hypothesis definition can lead to substantially different conclusions about the strength of evidence.
  • Accurate hypothesis formulation is necessary for reliable impact assessment of evidence.